ROME, Oct 3 (Reuters) - Italy is seeking clarity over rumours about European Central Bank (ECB) President Christine Lagarde possibly leaving her post early, Economy Minister Giancarlo Giorgetti said on Friday.

"I can't get inside President Lagarde's head, but I do think it's important to clarify this matter," Giorgetti told reporters during a press conference on the Treasury's new budget plan.

He also said Rome at present had no candidate to promote for the top ECB job.

Lagarde is due to officially depart by October of next year, although she is subject of persistent ​resignation rumours.

Spain is lobbying for Bank for International Settlements General Manager Pablo Hernandez de Cos to become the next ECB ​president, while the Netherlands is pushing for Klaas Knot, its former central bank chief.

"At the moment, there is no Italian candidate for the ECB, given that Italy has already achieved a major economic and diplomatic success with Carlo Comporti, the new president of ESMA, who will take office in the next few weeks," Giorgetti said.

ESMA is ​an independent ​EU ⁠agency based in Paris that acts as ​the EU's financial markets ​watchdog.

Asking not to be named, an Italian official told Reuters Rome might support the Spanish candidate, given Spain’s backing of Comporti.

However, the official said the debate within the right-wing ruling coalition was quite premature, and Prime Minister Giorgia Meloni would have the last say on the matter.

(Reporting by Giuseppe Fonte and Giselda Vagnoni, editing by Gavin Jones and Crispian Balmer)

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